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WORK IN PROGRESS - Need to check the code T-test (AI SL 4.11)

WORK IN PROGRESS - Need to check the code The Statisticians' Grand Prix

Scenario: The Statisticians' Grand Prix T-test (unpaired and population variance unknown) Background: Welcome to the annual Statisticians' Grand Prix, where the sharpest minds race to solve statistical challenges. This year's highlight is the "T-Test Trials," a thrilling event where contestants use an applet to conduct hypothesis tests and determine if their racing times significantly differ from the established standard. Objective: As a competitor, you will use the hypothesis testing applet to analyze your racing time data. Armed with your sample mean, standard deviation, and the Grand Prix standard time, you aim to prove that your average racing time is exceptional. Investigation Steps: 1. Setting the Stage: - Input your racing times as the sample mean and standard deviation into the applet. - Set the Grand Prix standard time as the population mean you're testing against. 2. Choosing Your Hypothesis: - Decide whether you want to prove your racing time is faster (a one-tailed test) or just different (a two-tailed test) from the standard. - Select the appropriate hypothesis in the applet. 3. Running the Numbers: - Determine the degrees of freedom based on your sample size. - Use the applet to calculate the t-statistic and the p-value for your sample data. 4. Crossing the Finish Line: - Interpret the p-value to conclude whether your racing times are statistically significant. - Present your findings to the Grand Prix judges. Questions for Investigation: 1. Discovery Question: - How does changing the significance level alter the outcome of your hypothesis test? 2. Strategy in Testing: - Why might a racer choose a one-tailed test over a two-tailed test or vice versa? 3. The Role of Sample Size: - How does increasing your sample size affect the reliability of your t-test results? 4. Reflection: - Reflect on the importance of hypothesis testing in competitive sports analytics.